I have two lists $L_1$ and $L_2$ of real numbers which are of equal length $n$ and I would like to analyze the complexity of the following problem: Select an index set $I\subseteq \{1,...,n\}$ with minimum cardinality such that $$\sum_{i \in I}L_1(i)\geq c_1$$ and $$\sum_{i \in I}L_2(i)\geq c_2$$ for two given constants $c_1$ and $c_2$.
The problem reminds me of some kind of subset sum problem but I can not find a reduction. I would be very grateful if someone could give me a hint for a reduction, a polynomial time algorithm or a dynamic programming approach for solving the problem.
For a dynamic programming approach, let value function $V(k,b_1,b_2)$ denote the minimum cardinality of $I\subseteq\{1,\dots,k\}$ such that $\sum_{i\in I} L_1(i) \ge b_1$ and $\sum_{i\in I} L_2(i) \ge b_2$. We want to compute $V(n,c_1,c_2)$. The DP recursion is $$V(k,b_1,b_2)=\min(V(k-1,b_1,b_2),1+V(k-1,b_1-L_1(k),b_2-L_2(k)))$$